Chemistry 2e · Atoms, Molecules, and Ions

Chemical Formulas

9 min read

Percent-composition example values are constructed for teaching; verify any real analytical data against current sources before relying on it.

On this page 9 sections

In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

A is the shorthand language of chemistry: it tells you which elements are present, how many atoms of each, and — for molecular compounds — how those atoms are connected. But not all formulas carry the same information. Molecular formulas state the actual number of atoms in one molecule (H₂O₂ for hydrogen peroxide). Empirical formulas give the simplest whole-number ratio of atoms (HO for hydrogen peroxide). Structural formulas show how the atoms are bonded together. Ionic compounds, which exist as extended networks rather than discrete molecules, are described by formula units — the smallest electrically neutral ratio of ions, such as CaCl₂ or Al₂O₃. Learning to read and write these formulas — and to derive empirical formulas from mass data — is the gateway to stoichiometry, the quantitative heart of chemistry.

Why this matters

Formulas are the difference between a recipe and a chemical identity. Water is H₂O; hydrogen peroxide is H₂O₂ — one extra oxygen atom changes a safe drink into a disinfectant, which is why misreading formulas is dangerous. The same shorthand underlies medication labels (NaCl for saline, NaHCO₃ for baking soda), fertilizer analysis (N-P-K), and industrial safety data sheets. Deriving empirical formulas from percent composition is also the classic "unknown compound" problem: forensic labs, quality-control chemists, and researchers all use the same method to identify what a substance is made of. For the nursing and health-science reader, recognizing that CaCO₃ (calcium carbonate) and CaCl₂ (calcium chloride) are different calcium salts — with very different uses — is exactly the kind of formula literacy that prevents medication errors.

The college version

Core Concepts

The formula family: molecular, empirical, structural

A uses subscripts to state the exact atom count per molecule: glucose is C₆H₁₂O₆ — 6 carbons, 12 hydrogens, 6 oxygens. An is the simplest whole-number ratio of atoms: dividing glucose's subscripts by 6 gives CH₂O. The empirical formula of glucose is therefore CH₂O — but so is the empirical formula of acetic acid (C₂H₄O₂), formaldehyde, and several other substances. Many different molecular formulas can share one empirical formula; the empirical formula alone cannot identify a compound. A adds connectivity — for water it is written H–O–H, showing both hydrogens bonded to the oxygen, not to each other. Condensed structural formulas (CH₃CH₂OH for ethanol) pack the same connectivity information into one line.

Molecular vs. empirical: the multiplier n

For any molecular compound, the molecular formula is a whole-number multiple of the empirical formula:

$molecular formula = n \times empirical formula, n = 1, 2, 3, \dots$

The multiplier n is found by comparing the compound's molar mass with its empirical formula mass:

$n = molar mass empirical formula mass$

When n = 1, the empirical and molecular formulas are the same, as with water (H₂O is already simplest) and methane (CH₄).

Deriving an empirical formula from mass data

Given the mass (or percent) of each element in a sample, the empirical formula comes from four steps:

Convert each element's mass to moles using its molar mass.
Divide every mole value by the smallest mole value.
If the results are not whole numbers, multiply all by the smallest integer that makes them whole.
Write the element symbols with those integers as subscripts.

The mole concept and molar masses are treated in detail in Chapter 3; here the method is introduced so the logic of formulas is clear from the start.

Formula units for ionic compounds

Ionic compounds do not form discrete molecules; they form repeating three-dimensional lattices of cations and anions. The is the smallest electrically neutral ratio of ions. It is dictated by charge balance: the total positive charge must equal the total negative charge. Sodium (Na⁺) and chloride (Cl⁻) give NaCl; calcium (Ca²⁺) and chloride (Cl⁻) give CaCl₂ because two chlorides are needed to balance one calcium. Aluminum (Al³⁺) and oxide (O²⁻) give Al₂O₃ — two Al³⁺ (total +6) balance three O²⁻ (total −6). A practical shortcut, the "criss-cross" method, takes the magnitude of each ion's charge as the of the other ion, then reduces the ratio to lowest terms.

Formulas encode more than atom counts

A formula can also carry structural hints: parentheses group polyatomic ions (Ca(NO₃)₂ contains two nitrate groups), and a dot in a formula shows incorporated water (CuSO₄ · 5H₂O is copper(II) sulfate pentahydrate — five waters per formula unit). Coefficients (numbers in front of formulas, like the 2 in 2H₂O) count molecules, not atoms within one molecule — a distinction that becomes critical when balancing equations.

Common Confusions

Do Not Confuse	With	Difference
Empirical formula	Molecular formula	Empirical is the simplest ratio (CH₂O); molecular is the actual atom count (C₆H₁₂O₆). Different compounds can share an empirical formula
H₂O	H₂O₂	Water vs. hydrogen peroxide — one extra O per molecule changes a stable beverage into an oxidizer. Formula literacy is a safety issue
Subscript	Coefficient	Subscript (in H₂O) counts atoms within one molecule; coefficient (in 2H₂O) counts whole molecules. 2H₂O = 4 H atoms total
Ca(NO₃)₂	CaNO₃	The parentheses mean TWO nitrate groups — 2 N and 6 O atoms. Dropping parentheses loses the polyatomic ion's identity
Formula unit	Molecule	Ionic compounds have no discrete molecules; the formula unit is just the smallest neutral ion ratio. Molecular formulas apply only to covalent compounds
Changing a formula	Balancing an equation	You never change subscripts to balance an equation (that changes the substance); you change coefficients only
Hydrate dot	Multiplication	The dot in CuSO₄ · 5H₂O means "with 5 waters," not multiplication — the formula unit includes 5 water molecules

Eli explains

The same idea, in plain words

Explain it like I’m 10

A chemical formula is like a LEGO instruction card. It tells you how many of each brick to use: H₂O means two hydrogen bricks and one oxygen brick. Sometimes the card shows the simplest recipe — "1 of each" — while the real toy needs more, like how both a tiny and a giant snowman can be built from "1 head + 1 body" repeated different numbers of times. Ionic compounds are different: they're like a wall of bricks where plus-bricks and minus-bricks must balance perfectly, so the formula just tells you how many of each kind you need to make a stable wall. Reading the card correctly — and not mistaking H₂O for H₂O₂ — is the whole game.

Worked example

Example 1 — Empirical from molecular. Glucose has the molecular formula C₆H₁₂O₆. Find its empirical formula, and determine the multiplier n.

Divide every subscript by the greatest common divisor (6):

$C 6 H 12 O 6 \to C 6/6 H 12/6 O 6/6 = CH 2 O$

So the empirical formula is CH₂O and the multiplier is:

$n = 61 = 6$

Check: acetic acid (C₂H₄O₂) has the same empirical formula CH₂O with n = 2 — proof that empirical formulas alone cannot identify a compound.

Example 2 — Empirical formula from percent composition. A compound is 40.00% carbon, 6.71% hydrogen, and 53.29% oxygen by mass. Determine its empirical formula.

Assume a 100.0 g sample, so percentages become grams: 40.00 g C, 6.71 g H, 53.29 g O. Convert each to moles (using molar masses 12.01, 1.008, and 16.00 g/mol):

$n C = 40.00 g 12.01 g/mol = 3.331 mol$

$n H = 6.71 g 1.008 g/mol = 6.657 mol$

$n O = 53.29 g 16.00 g/mol = 3.331 mol$

Divide each by the smallest value (3.331):

$C: 3.331 3.331 = 1, H: 6.657 3.331 = 1.998 \approx 2, O: 3.331 3.331 = 1$

The ratio is 1 : 2 : 1, so the empirical formula is CH₂O. If the compound's molar mass were later measured as 180 g/mol, the molecular formula would be:

$n = 180 g/mol 30.03 g/mol = 6 \to C 6 H 12 O 6$

Example 3 — Formula unit from charges. Write the formula unit for the ionic compound formed from aluminum (Al³⁺) and oxide (O²⁻) ions.

The total charge must be zero. Two Al³⁺ give +6; three O²⁻ give −6:

$2(+3) + 3(-2) = 0$

So the formula unit is Al₂O₃. The criss-cross shortcut gives the same result: take the charge magnitude of Al (3) as the subscript of O, and the magnitude of O (2) as the subscript of Al, writing Al₂O₃ — already in lowest terms.

Key takeaways

Molecular formula: exact atom count per molecule (C₆H₁₂O₆); empirical formula: simplest whole-number ratio (CH₂O); structural formula: shows connectivity (H–O–H).
Many molecules share one empirical formula; the empirical formula alone cannot identify a compound.
molecular formula = n × empirical formula, with n = molar massempirical formula mass.
Empirical formula from data: mass → moles → divide by smallest → multiply to whole numbers.
Ionic compounds are described by formula units (smallest neutral ion ratio), governed by charge balance: CaCl₂, Al₂O₃, Na₂SO₄.
Criss-cross shortcut: charge magnitude of one ion becomes the subscript of the other, then reduce.
Parentheses enclose polyatomic ions; a dot in a hydrate (e.g., CuSO₄ · 5H₂O) means incorporated water.
Subscripts count atoms inside a formula; coefficients count whole formulas (molecules) in front.
Exam trap: H₂O₂ (hydrogen peroxide, empirical HO) vs H₂O (water, empirical H₂O) — different compounds, different properties.

Check yourself

5 review questions from the chapter. Try each one, then open the answer.

What is the empirical formula of butane, C₄H₁₀? Of benzene, C₆H₆?
Show answer
Butane: divide C₄H₁₀ by 2 → C₂H₅. Benzene: divide C₆H₆ by 6 → CH. (Note: benzene's empirical formula is CH — its molecular formula is six times that.)
A compound is 27.06% sodium, 16.47% nitrogen, and 56.47% oxygen by mass. What is its empirical formula?
Show answer
In a 100.0 g sample: Na = 27.06/22.99 = 1.177 mol; N = 16.47/14.01 = 1.176 mol; O = 56.47/16.00 = 3.529 mol. Divide by 1.176: Na 1, N 1, O 3 → NaNO₃ (sodium nitrate).
Why can two different compounds have the same empirical formula, and what information resolves which is which?
Show answer
Because the empirical formula only records the simplest ratio — e.g., CH₂O fits glucose, acetic acid, and formaldehyde. The molecular formula (or the molar mass) resolves the identity: n = molar mass/empirical formula mass.
Write the formula unit for the compound of calcium (Ca²⁺) and phosphate (PO₄^3-).
Show answer
Charge balance: 3 Ca²⁺ (+6) with 2 PO₄^3- (−6) → Ca₃(PO₄)₂ — the familiar mineral form of calcium phosphate.
How many hydrogen atoms are represented by 3NH₄NO₃? How many nitrate groups?
Show answer
Each NH₄NO₃ has 4 H atoms, so 3 × 4 = 12 hydrogen atoms total. Each formula unit has one nitrate group (NO₃^-), so 3 nitrate groups.

Keep learning

Ready to build on this? Continue to the next lesson.

Study tools & related lessonsKey vocabulary · Related

Key vocabulary

Chemical formula: Symbolic description of a substance's composition using element symbols and subscripts
Molecular formula: Exact numbers of each atom in one molecule
Empirical formula: Simplest whole-number ratio of atoms in a compound
Structural formula: Shows which atoms are bonded to which
Formula unit: Smallest electrically neutral ratio of ions in an ionic compound
Polyatomic ion: A group of atoms with an overall charge, e.g., NO₃^-, SO₄^2-
Hydrate: An ionic compound with incorporated water, e.g., CuSO₄ · 5H₂O
Coefficient: A number in front of a formula counting whole molecules, e.g., the 2 in 2H₂O
Subscript: A number within a formula counting atoms of the preceding element

Sources & references

openstax.org — Chemistry 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

Educational content only. It is not medical, legal or professional advice. Found an error? Tell us.

In 30 seconds

Why this matters

The college version

Core Concepts

The formula family: molecular, empirical, structural

Molecular vs. empirical: the multiplier n

Deriving an empirical formula from mass data

Formula units for ionic compounds

Formulas encode more than atom counts

Common Confusions

The same idea, in plain words

Worked example

Key takeaways

Check yourself

Keep learning

Key vocabulary

Related lessons

Sources & references